Stochastic Process

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L Amati - One of the best experts on this subject based on the ideXlab platform.

  • a common Stochastic Process rules gamma ray burst prompt emission and x ray flares
    The Astrophysical Journal, 2015
    Co-Authors: C Guidorzi, S Dichiara, F Frontera, R Margutti, A Baldeschi, L Amati
    Abstract:

    Prompt‐ray and early X‐ray afterglow emission in gamma‐ray bursts (GRBs) are characterized by a bursty behavior and are often interspersed with long quiescent times. There is compelling evidence that X‐ray flares are linked to prompt ‐rays. However, the physical mechanism that leads to the complex temporal distribution of ‐ray pulses and X‐ray flares is not understood. Here we show th at the waiting time distribution (WTD) of pulses and flares exhibits a power‐law tail extending over 4 decades with index ∼ 2 and can be the manifestation of a common time‐dependent Poisson Process. This result is robust and is obtained on different catalogs. Surprisingly, GRBs with many (≥ 8) ‐ray pulses are very unlikely to be accompanied by X‐ray flares after the end of the prompt emission (3 .1� Gaussian confidence). These results are consistent with a simple interpretation: an hyperaccreting disk breaks up in to one or a few groups of fragments, each of which is independently accreted with the same probability per unit time. Prompt ‐rays and late X‐ray flares are nothing but different fragments being accreted at the beginning and at the end, respectively, following the very same Stochastic Process and likely the same mechanism. Subject headings:gamma-ray: bursts, waiting time distribution

  • a common Stochastic Process rules gamma ray burst prompt emission and x ray flares
    arXiv: High Energy Astrophysical Phenomena, 2015
    Co-Authors: C Guidorzi, S Dichiara, F Frontera, R Margutti, A Baldeschi, L Amati
    Abstract:

    Prompt gamma-ray and early X-ray afterglow emission in gamma-ray bursts (GRBs) are characterized by a bursty behavior and are often interspersed with long quiescent times. There is compelling evidence that X-ray flares are linked to prompt gamma-rays. However, the physical mechanism that leads to the complex temporal distribution of gamma-ray pulses and X-ray flares is not understood. Here we show that the waiting time distribution (WTD) of pulses and flares exhibits a power-law tail extending over 4 decades with index ~2 and can be the manifestation of a common time-dependent Poisson Process. This result is robust and is obtained on different catalogs. Surprisingly, GRBs with many (>=8) gamma-ray pulses are very unlikely to be accompanied by X-ray flares after the end of the prompt emission (3.1 sigma Gaussian confidence). These results are consistent with a simple interpretation: an hyperaccreting disk breaks up into one or a few groups of fragments, each of which is independently accreted with the same probability per unit time. Prompt gamma-rays and late X-ray flares are nothing but different fragments being accreted at the beginning and at the end, respectively, following the very same Stochastic Process and likely the same mechanism.

F Frontera - One of the best experts on this subject based on the ideXlab platform.

  • a common Stochastic Process rules gamma ray burst prompt emission and x ray flares
    The Astrophysical Journal, 2015
    Co-Authors: C Guidorzi, S Dichiara, F Frontera, R Margutti, A Baldeschi, L Amati
    Abstract:

    Prompt‐ray and early X‐ray afterglow emission in gamma‐ray bursts (GRBs) are characterized by a bursty behavior and are often interspersed with long quiescent times. There is compelling evidence that X‐ray flares are linked to prompt ‐rays. However, the physical mechanism that leads to the complex temporal distribution of ‐ray pulses and X‐ray flares is not understood. Here we show th at the waiting time distribution (WTD) of pulses and flares exhibits a power‐law tail extending over 4 decades with index ∼ 2 and can be the manifestation of a common time‐dependent Poisson Process. This result is robust and is obtained on different catalogs. Surprisingly, GRBs with many (≥ 8) ‐ray pulses are very unlikely to be accompanied by X‐ray flares after the end of the prompt emission (3 .1� Gaussian confidence). These results are consistent with a simple interpretation: an hyperaccreting disk breaks up in to one or a few groups of fragments, each of which is independently accreted with the same probability per unit time. Prompt ‐rays and late X‐ray flares are nothing but different fragments being accreted at the beginning and at the end, respectively, following the very same Stochastic Process and likely the same mechanism. Subject headings:gamma-ray: bursts, waiting time distribution

  • a common Stochastic Process rules gamma ray burst prompt emission and x ray flares
    arXiv: High Energy Astrophysical Phenomena, 2015
    Co-Authors: C Guidorzi, S Dichiara, F Frontera, R Margutti, A Baldeschi, L Amati
    Abstract:

    Prompt gamma-ray and early X-ray afterglow emission in gamma-ray bursts (GRBs) are characterized by a bursty behavior and are often interspersed with long quiescent times. There is compelling evidence that X-ray flares are linked to prompt gamma-rays. However, the physical mechanism that leads to the complex temporal distribution of gamma-ray pulses and X-ray flares is not understood. Here we show that the waiting time distribution (WTD) of pulses and flares exhibits a power-law tail extending over 4 decades with index ~2 and can be the manifestation of a common time-dependent Poisson Process. This result is robust and is obtained on different catalogs. Surprisingly, GRBs with many (>=8) gamma-ray pulses are very unlikely to be accompanied by X-ray flares after the end of the prompt emission (3.1 sigma Gaussian confidence). These results are consistent with a simple interpretation: an hyperaccreting disk breaks up into one or a few groups of fragments, each of which is independently accreted with the same probability per unit time. Prompt gamma-rays and late X-ray flares are nothing but different fragments being accreted at the beginning and at the end, respectively, following the very same Stochastic Process and likely the same mechanism.

Rosario N Mantegna - One of the best experts on this subject based on the ideXlab platform.

  • Stochastic Process with ultraslow convergence to a gaussian the truncated levy flight
    Physical Review Letters, 1994
    Co-Authors: Rosario N Mantegna, Eugene H Stanley
    Abstract:

    We introduce a class of Stochastic Process, the truncated L\'evy flight (TLF), in which the arbitrarily large steps of a L\'evy flight are eliminated. We find that the convergence of the sum of $n$ independent TLFs to a Gaussian Process can require a remarkably large value of $n$---typically $n\ensuremath{\approx}{10}^{4}$ in contrast to $n\ensuremath{\approx}10$ for common distributions. We find a well-defined crossover between a L\'evy and a Gaussian regime, and that the crossover carries information about the relevant parameters of the underlying Stochastic Process.

  • Stochastic Process with ultraslow convergence to a gaussian the truncated levy flight
    Physical Review Letters, 1994
    Co-Authors: Rosario N Mantegna, H E Stanley
    Abstract:

    We introduce a class of Stochastic Process, the [ital truncated] Levy flight (TLF), in which the arbitrarily large steps of a Levy flight are eliminated. We find that the convergence of the sum of [ital n] independent TLFs to a Gaussian Process can require a remarkably large value of [ital n]---typically [ital n][approx]10[sup 4] in contrast to [ital n][approx]10 for common distributions. We find a well-defined crossover between a Levy and a Gaussian regime, and that the crossover carries information about the relevant parameters of the underlying Stochastic Process.

H E Stanley - One of the best experts on this subject based on the ideXlab platform.

  • Stochastic Process with ultraslow convergence to a gaussian the truncated levy flight
    Physical Review Letters, 1994
    Co-Authors: Rosario N Mantegna, H E Stanley
    Abstract:

    We introduce a class of Stochastic Process, the [ital truncated] Levy flight (TLF), in which the arbitrarily large steps of a Levy flight are eliminated. We find that the convergence of the sum of [ital n] independent TLFs to a Gaussian Process can require a remarkably large value of [ital n]---typically [ital n][approx]10[sup 4] in contrast to [ital n][approx]10 for common distributions. We find a well-defined crossover between a Levy and a Gaussian regime, and that the crossover carries information about the relevant parameters of the underlying Stochastic Process.

C Guidorzi - One of the best experts on this subject based on the ideXlab platform.

  • a common Stochastic Process rules gamma ray burst prompt emission and x ray flares
    The Astrophysical Journal, 2015
    Co-Authors: C Guidorzi, S Dichiara, F Frontera, R Margutti, A Baldeschi, L Amati
    Abstract:

    Prompt‐ray and early X‐ray afterglow emission in gamma‐ray bursts (GRBs) are characterized by a bursty behavior and are often interspersed with long quiescent times. There is compelling evidence that X‐ray flares are linked to prompt ‐rays. However, the physical mechanism that leads to the complex temporal distribution of ‐ray pulses and X‐ray flares is not understood. Here we show th at the waiting time distribution (WTD) of pulses and flares exhibits a power‐law tail extending over 4 decades with index ∼ 2 and can be the manifestation of a common time‐dependent Poisson Process. This result is robust and is obtained on different catalogs. Surprisingly, GRBs with many (≥ 8) ‐ray pulses are very unlikely to be accompanied by X‐ray flares after the end of the prompt emission (3 .1� Gaussian confidence). These results are consistent with a simple interpretation: an hyperaccreting disk breaks up in to one or a few groups of fragments, each of which is independently accreted with the same probability per unit time. Prompt ‐rays and late X‐ray flares are nothing but different fragments being accreted at the beginning and at the end, respectively, following the very same Stochastic Process and likely the same mechanism. Subject headings:gamma-ray: bursts, waiting time distribution

  • a common Stochastic Process rules gamma ray burst prompt emission and x ray flares
    arXiv: High Energy Astrophysical Phenomena, 2015
    Co-Authors: C Guidorzi, S Dichiara, F Frontera, R Margutti, A Baldeschi, L Amati
    Abstract:

    Prompt gamma-ray and early X-ray afterglow emission in gamma-ray bursts (GRBs) are characterized by a bursty behavior and are often interspersed with long quiescent times. There is compelling evidence that X-ray flares are linked to prompt gamma-rays. However, the physical mechanism that leads to the complex temporal distribution of gamma-ray pulses and X-ray flares is not understood. Here we show that the waiting time distribution (WTD) of pulses and flares exhibits a power-law tail extending over 4 decades with index ~2 and can be the manifestation of a common time-dependent Poisson Process. This result is robust and is obtained on different catalogs. Surprisingly, GRBs with many (>=8) gamma-ray pulses are very unlikely to be accompanied by X-ray flares after the end of the prompt emission (3.1 sigma Gaussian confidence). These results are consistent with a simple interpretation: an hyperaccreting disk breaks up into one or a few groups of fragments, each of which is independently accreted with the same probability per unit time. Prompt gamma-rays and late X-ray flares are nothing but different fragments being accreted at the beginning and at the end, respectively, following the very same Stochastic Process and likely the same mechanism.